Details

series2.0m (36.8%)

Calls

430 calls:

5.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) 1) (/ 2.0 2))) (pow (/ (cbrt l) Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (26.3%)

Algorithm
61×intervals
Results
15.8s29350×body1280valid
15.0s253224×body80valid
9.3s158091×body80nan
8.8s8786×body2560valid
7.3s20641×body640valid
5.1s3346×body5120valid
2.4s9945×body320valid
1.3s9119×body160valid
400.0ms677×body10240exit
145.0ms617×body1280nan
113.0ms615×body640nan
110.0ms8256×pre80true
46.0ms340×body320nan
19.0ms195×body160nan

prune55.7s (17.3%)

rewrite35.6s (11.1%)

Algorithm
116×rewrite-expression-head
Calls

430 calls:

2.8s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
2.7s
(* (* (* (* (* (pow (cbrt t) 3.0) (/ (pow (cbrt t) 3.0) l)) (/ (pow t (* 1/3 3.0)) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.4s
(/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar))
942.0ms
(/ (sqrt NdChar) (/ (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))) (sqrt NdChar)))
926.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
Rules
53407×add-exp-log
39561×prod-exp
27266×pow-exp
18709×div-exp
12527×pow-to-exp
4114×add-sqr-sqrt
4113×1-exp
4073×rec-exp
3691×*-un-lft-identity
3458×times-frac
3034×add-cube-cbrt
2381×add-cbrt-cube
1579×sqrt-prod
1306×pow1
1103×cbrt-prod
1022×cbrt-unprod
897×associate-*r*
810×associate-*r/
792×unpow-prod-down
647×associate-*l*
502×add-log-exp
449×sqrt-div
430×log1p-expm1-u expm1-log1p-u
429×pow-prod-down
413×frac-times
378×cbrt-undiv
355×associate-*l/
353×cbrt-div
352×associate-/l*
340×pow-unpow
338×prod-diff
326×flip-- flip3--
320×associate-/r*
274×unswap-sqr
246×difference-of-squares
243×sqr-pow
238×associate-/r/
235×div-inv
202×distribute-lft-out
179×distribute-rgt-in distribute-lft-in
178×distribute-lft-out--
147×*-commutative
146×flip-+ flip3-+
135×distribute-rgt-neg-in
124×pow1/3
108×distribute-lft-neg-in
95×swap-sqr
90×clear-num frac-2neg
73×tan-quot
70×fma-def
56×sub-neg
55×sqrt-pow1
54×pow-prod-up
51×pow-pow
45×rem-sqrt-square
42×associate--l+
40×pow1/2 pow-sqr
39×associate-/l/
35×sum-log
34×cube-div
33×frac-sub
31×unpow2
27×pow-plus
25×fma-udef
24×div-sub
23×cos-sum
22×pow2
20×pow-sub +-commutative
19×pow-neg
17×neg-sub0
16×exp-diff frac-add log-div
14×un-div-inv
13×hypot-def
12×neg-mul-1
11×fma-neg
10×exp-prod
9×log-prod
8×exp-neg log-pow cube-prod distribute-rgt-neg-out
6×exp-sum
5×diff-log
4×rem-cube-cbrt mul-1-neg associate-+l+ associate-+r+ unpow3 cube-mult distribute-neg-frac log-rec
3×inv-pow unsub-neg pow-flip associate-+r- neg-log
2×hypot-udef distribute-frac-neg acos-asin
1×rem-exp-log sqrt-undiv unpow1/3 cos-diff mul0 rem-log-exp rem-cbrt-cube

simplify12.6s (3.9%)

Algorithm
176×egg-herbie

regimes9.7s (3.0%)

Accuracy

Total 42.3b remaining (22.4%)

Threshold costs 3.8b (2%)

7.9b22.9%Toniolo and Linder, Equation (13)
6.3b3.8%Henrywood and Agarwal, Equation (12)
6.0b8.5%Toniolo and Linder, Equation (10+)
5.0b78.6%Toniolo and Linder, Equation (7)
4.7b27.4%Toniolo and Linder, Equation (10-)

bsearch2.8s (0.9%)

localize2.3s (0.7%)

end0.0ms (0.0%)